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Theorem 19.29 1914
 Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1915. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
19.29 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))

Proof of Theorem 19.29
StepHypRef Expression
1 pm3.2 462 . . 3 (𝜑 → (𝜓 → (𝜑𝜓)))
21aleximi 1872 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥(𝜑𝜓)))
32imp 444 1 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∀wal 1594  ∃wex 1817 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818 This theorem is referenced by:  19.29x  1917  supsrlem  10045  1stccnp  21388  iscmet3  23212  isch3  28328  bnj849  31223  axc11n11r  32900  stoweidlem35  40672
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